An Approach to Savitzky–Golay Differentiators

Figueiredo, Natanael S.; Ferreira, Luís H. C.; Dutra, Odilon O.

doi:10.1007/s00034-019-01045-w

Cited by 5 publications

(7 citation statements)

References 10 publications

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“…6) (iterative procedure). 3,9,14,32 The remaining residuals r are believed to express the refused, unwanted discrepancy of data. Instead of fitting the polynomials, a more robust method of moving average computation ((Eq.…”

Section: Filtering Of Spectramentioning

confidence: 99%

“…9 Although the Savitzky-Golay filter is undoubtedly an extremely useful tool (and thus has become a "monopolist" in the spectral processing domain), it has been reported 1 Jagiellonian University in Kraków Faculty of Chemistry, Krakow, Poland to have some drawbacks, too. [10][11][12][13][14][15] Even though a variety of upgrades have been introduced to increase its efficiency, 14,[16][17][18] yet, some limitations related to the very core of the algorithm still remain impossible to be fully resolved. For the above reasons, the Authors believe that alternative concepts of spectral processing should deserve more attention.…”

Section: Introductionmentioning

confidence: 99%

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Searching for Alternatives to the Savitzky–Golay Filter in the Spectral Processing Domain

Kałka

Turek

2023

Appl Spectrosc

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An elegant, well-established effective data filter concept, proposed originally by Abraham Savitzky and Marcel J.E. Golay, is undoubtedly a very effective tool, however not free from limitations and drawbacks. Despite the latter, over the years it has become a "monopolist” in many fields of spectra processing, claiming a "commercial" superiority over alternative approaches, which would potentially allow to obtain equivalent or in some cases even more reliable results. In order to show that basic operations performed on spectral datasets, like smoothing or differentiation, do not have to be equated to the application of the one particular single algorithm, several of such alternatives are briefly presented within this paper and discussed with regard to their practical realization. A special emphasis is put on the fast Fourier methodology (FFT), being widespread in the general domain of signal processing. Finally, a user-friendly Matlab routine, in which the outlined algorithms are implemented, is shared, so that one can select and apply the technique of spectral data processing more adequate for their individual requirements without the need to code it prior to use.

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Section: Filtering Of Spectramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Searching for Alternatives to the Savitzky–Golay Filter in the Spectral Processing Domain

Kałka

Turek

2023

Appl Spectrosc

View full text Add to dashboard Cite

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“…In the present work, we use numerical differentiation by simply taking z i +1 – z i , which is closer to analytic differentiation than the method mentioned above. This numerical method may be unsuitable for some applications because it causes a shift by 1/2 data point; then the above method 12 must be used. For most purposes, the difference between the differentiation methods is irrelevant (except for differences in the noise suppression of the traditional SG filters).…”

Section: Applicationsmentioning

confidence: 99%

“…4 Since SG filters are based on a polynomial fit, the derivative can be calculated analytically, making SG filtering popular for this application. It has been noted previously 12 that essentially the same can be accomplished by SG filtering followed by numeric differentiation, with a slight improvement of noise suppression when calculating the derivative of the filtered data z as (z i+1 − z i−1 )/2. The slightly improved noise suppression is mainly due to the difference between the frequency response of analytic differentiation (multiplication with ω) and that of the numerical derivative (multiplication with sin ω when taking the sampling frequency as f s = 1).…”

Section: Smoothing For Calculating the Derivativesmentioning

confidence: 99%

“…When reading the literature about SG filters, one could get the impression that the unsatisfactory suppression of frequencies above the cutoff is the price to pay for the flat frequency response in the passband, and that the room for improvements is limited. , Most recent developments regarding SG filters focus on adaptive SG filtering and adjusting the filter parameters to best fit the signal and noise of a given data set, ,, not on improving the filter. In this paper, we show that a flat passband can still be achieved while the stopband is strongly attenuated.…”

Section: Introductionmentioning

confidence: 99%

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Why and How Savitzky–Golay Filters Should Be Replaced

2022

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Savitzky–Golay (SG) filtering, based on local least-squares fitting of the data by polynomials, is a popular method for smoothing data and calculations of derivatives of noisy data. At frequencies above the cutoff, SG filters have poor noise suppression; this unnecessarily reduces the signal-to-noise ratio, especially when calculating derivatives of the data. In addition, SG filtering near the boundaries of the data range is prone to artifacts, which are especially strong when using SG filters for calculating derivatives of the data. We show how these disadvantages can be avoided while keeping the advantageous properties of SG filters. We present two classes of finite impulse response (FIR) filters with substantially improved frequency response: (i) SG filters with fitting weights in the shape of a window function and (ii) convolution kernels based on the sinc function with a Gaussian-like window function and additional corrections for improving the frequency response in the passband (modified sinc kernel). Compared with standard SG filters, the only price to pay for the improvement is a moderate increase in the kernel size. Smoothing at the boundaries of the data can be improved with a non-FIR method, the Whittaker–Henderson smoother, or by linear extrapolation of the data, followed by convolution with a modified sinc kernel, and we show that the latter is preferable in most cases. We provide computer programs and equations for the smoothing parameters of these smoothers when used as plug-in replacements for SG filters and describe how to choose smoothing parameters to preserve peak heights in spectra.

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